The present invention is directed to a method and apparatus for predicting stability characteristics of power supplies or other closed loop systems under arbitrary load conditions. The present invention is particularly directed to a method for predicting stability characteristics for direct current, DC-to-DC, power supplies.
When designing certain systems, such as power supply, or power converter circuits, one must take into account the potential user""s load characteristics. This consideration is especially important in the design of DC-DC converters because such converters are generally configured as a closed loop system that monitors its output, provides feedback indicating its output, and employs the feedback to adjust to maintain a constant DC output. In any feedback system, it is of significant importance that the feedback loop be stable. A simple example of an unstable feedback loop is the loud tone produced in the presence of audio feedback when a microphone is placed too close to a speaker producing signals originating at the microphone.
Today""s electronic devices are more and more designed to be faster, smaller, and more reliable. This trend for product requirements is especially evident in portable electronic devices such as cellular telephones, electronic games, and portable computers. Some practical design consequences of this trend are that output voltages for DC-DC converters are getting lower and the stability of output of DC-DC converters is more difficult to attain for certain loads or applications.
The fact that a user""s load characteristics figure so intimately in stability of DC-DC converter circuits, and the ever more stringent requirements for greater stability at lower voltages for modem electronic circuits have made present ways of predicting stability of a particular DC-DC converter circuit for a particular application uneconomical and not particularly reliable or accurate.
Nyquist developed criteria to assess the stability of a control loop (xe2x80x9cRegeneration Theoryxe2x80x9d, H. Nyquist, Bell System Technical Journal, January 1932). Bode (xe2x80x9cRelations Between Attenuation and Phase in Feedback Amplifier Designxe2x80x9d, Bell System Technical Journal, July 1940) expressed these criteria in terms of the phase (xcfx86) and gain of a transfer function. According to this analysis, if gain (dB) and phase change (xcex94xcfx86) of the loop gain are zero at the same frequency in a circuit, the circuit will be unstable.
As a practical engineering measure, one must design a circuit having xe2x89xa745xc2x0 phase margin to reliably have a stable circuit. Phase margin is the value of phase when gain as a function of frequency crosses through zero from positive to negative. Thus, when gain is 0 dB, and gain is passing from positive to negative, phase must be xe2x89xa745xc2x0 in order for the circuit under consideration to be stable with adequate margin.
Another measure of stability is to require that gain margin be xe2x89xa7xe2x88x927 to xe2x88x9210 dB. That is, when phase as a function of frequency crosses through zero, gain must be at least 7-10 dB in order that the circuit under consideration will be a stable circuit.
Presently, manufacturers of power supplies, and especially of DC-DC converters, use simulations, or laboratory measurements, or closed form analytical expressions, or all three of those methods for determining whether a particular circuit is stable with a particular load. Simulations are expensive in that they occupy large amounts of computer capacity and time. Closed form analytical expressions rely on simplifying assumptions that introduce significant errors. Laboratory measurements are an expensive approach to answering questions about a particular circuit-load stability in terms of human time and computer assets involved. Further, neither simulations, closed form analytical expressions nor laboratory experimentation are particularly accurate in predicting stability of converter apparatuses under various load conditions.
One result of ongoing efforts to predict stability with arbitrary loads is that manufacturers of power converters must essentially custom-tailor their products to user""s loads on a case-by-case basis. Such a xe2x80x9cjob shopxe2x80x9d approach to production precludes one""s taking advantage of the economies of scale which could be enjoyed if a manufacturer could predict which loads were amenable to stable use with particular converters. That is, if manufacturers could predict stability for a particular converter circuit for a particular load without having to physically evaluate the converter circuit with the particular load, then the inefficiencies of customizing converter circuits for each discrete load criterion may be avoided. Manufacturers enjoying such an advantage in predictability of stability of their products vis-xc3xa1-vis loads may produce converter apparatuses for xe2x80x9coff-the-shelfxe2x80x9d availability to customers with evaluation tools enabling customers to select which of the converters will accommodate the particular loads they are designing.
There is a need for a method for predicting stability characteristics of power converters under arbitrary load conditions. This need is particularly acute in predicting stability characteristics of DC-DC power converter circuits.
It would be particularly useful if stability characteristics of power supply apparatuses could be predicted without having to test the power supply apparatus under the particular load condition for which a stability determination is desired.
The method of the present invention allows evaluation of the stability of a power supply apparatus for various load conditions without having to recharacterize the apparatus for each given load.
A method for predicting stability of a closed loop apparatus is disclosed. The closed loop apparatus has an open loop impedance and at least one inherent internal gain. The method comprises the steps of: (a) identifying an impedance scaling factor associated with the closed loop apparatus that may be expressed in terms including the open loop impedance, the at least one inherent internal gain, a gain variable and a phase variable; (b) vectorally establishing a first scaling value for the impedance scaling factor as a function of frequency while maintaining a first variable of the gain variable and the phase variable at a first working value to record the first scaling value for a plurality of frequencies. The method may include the further steps of: (c) vectorally establishing a second scaling value for the impedance scaling factor as a function of frequency while maintaining a second variable of the gain variable and the phase variable at a second working value to record the second scaling value for a plurality of frequencies. The apparatus comprises a first reference tool relating the first scaling value with the second variable of the gain variable and the phase variable as a function of frequency. The apparatus may further comprise a second reference tool relating the second scaling value with the first variable of the gain variable and the phase variable as a function of frequency.
The stability of a controlled apparatus, that is an apparatus with regeneration or feedback, such as a regulated power supply, power converter, amplifier or other closed loop apparatus, is an important, if not critical, consideration in any application of that apparatus. Measures of the stability or potential stability of a controlled apparatus include the phase margin and the gain margin. Preferably, both the phase margin and the gain margin of an apparatus are considered in evaluating the stability of the apparatus. Such margin measures are an indication of how close the control system or the loop response of that apparatus is to instability. The loop response itself is a function of the load placed on the output of such an apparatus.
The conventional approach to evaluate or determine the margins of such an apparatus has been to generate a Bode plot of the loop response for a specific load condition. By inspection of such a Bode plot one may determine the value of the margin of the apparatus being evaluated for that specific load condition. In the case where the load is to be designed appropriately to maintain the apparatus in a stable condition during operation, the conventional approach has resulted in a time consuming process of iterations of load adjustments, Bode plot generation for each adjustment, inspection and readjustment. By such iterative employment of the conventional approach, one may step-wise ascertain a load that permits stable operation of an apparatus.
The preferred embodiment of the present invention produces a response plot of a closed loop apparatus that is not dependent on the load characteristics with which the apparatus is to be employed for the basic plot generation. As a result, the same plot can be used to determine the operating margin of the apparatus characterized by the plot for any variation of the load with which the apparatus is to be employed. Such a load-independent evaluation method can significantly reduce the effort of characterizing the response of a power supply apparatus for a given load.
Features of the present invention will be apparent from the following specification and claims when considered in connection with the accompanying drawings, in which like elements are labeled using like reference numerals in the various figures, illustrating the preferred embodiment of the invention.